Answer
Diana has 300 dimes
Explanation:
The coin is the combination of nickels and dimes
Let x represents nickels
Let y represents dimes
Since the total coin is 500
x + y = 500 ------------ equation 1
The total value of the coin is $40
0.05x + 0.1y = 40 ------------- equation 2
Solve equations 1 and 2 simultaneously using the substitution method
x + y = 500 --------- equation 1
0.05x + 0.1y = 40 - equation 2
Isolate x in equation 1
x = 500 - y
Substitute the value of x in equation 2
0.05(500 - y) + 0.1y = 40
Open the parenthesis
25 - 0.05y + 0.1y = 40
Collect the like terms
-0.05y + 0.1y = 40 - 25
0.05y = 15
Isolate y by dividing through by 0.05
0.05y/0.05 = 15/0.05
y = 300
Hence, Diana has 300 dimes